Perturbations of Drazin invertible operators

Abstract

The necessary and sufficient conditions for the small norm perturbation of a Drazin invertible operator to be still Drazin invertible and the sufficient conditions for the finite rank perturbation of a Drazin invertible operator to be still Drazin invertible are established.

Keywords

Drazin inverse / small norm perturbation / finite rank perturbation

References

[1] Ben-Israel A, Greville T N E. Generalized Inverses: Theory and Applications. New York: Wiley-Interscience, 1974

[2] Campbell S L, Meyer C D. Generalized Inverses of Linear Transformations. New York: Dover, 1991

[3] Castro-González N. Additive perturbation results for the Drazin inverse. Linear Algebra Appl, 2005, 397: 279-297

[4] Castro-González N, Vélez-Cerrada J. Characterizations of matrices which eigenprojections at zero are equal to a fixed perturbation. Appl Math Comput, 2004, 159: 613-623

[5] Castro-González N, Koliha J J. Perturbation of the Drazin inverse for closed linear operators. Integral Equations Operator Theory, 2000, 36: 92-106

[6] Castro-González N, Koliha J J, Wei Yimin. Perturbation of the Drazin inverse for matrices with equal eigenprojections at zero. Linear Algebra Appl, 2000, 312: 181-189

[7] Conway J B. A Course in Functional Analysis. 2nd ed. Berlin: Springer-Verlag, 1990

[8] Diao H. Structured perturbations of Drazin inverse. Appl Math Comput, 2004, 158: 419-432

[9] Du Hong Ke, Deng Chun Yuan. The representation and characterization of Drazin inverses of operators on a Hilbert space. Linear Algebra Appl, 2005, 407: 117-124

[10] Hartwig R E, Wang G, Wei Y. Some additive results on Drazin inverses. Linear Algebra Appl, 2001, 322: 207-217

[11] Li X, Wei Y. A note on the perturbation bound of the Drazin inverse. Appl Math Comput, 2003, 140: 329-340

[12] Taylar A E, Lay D C. Introduction to Functional Analysis. 2nd ed. New York: John Wiley & Sons, 1980

[13] Wei Y. Perturbation bound of the Drazin inverse. Appl Math Comput, 2002, 125: 231-244

[14] Wei Y. The Drazin inverse of updating of a square matrix with application to perturbation formula. Appl Math Comput, 2000, 108: 77-83

[15] Wei Y, Qiao S. The representation and approximation of the Drazin inverse of a linear operator in Hilbert space. Appl Math Comput, 2003, 138: 77-89

[16] Wei Y, Wang G. The perturbation theory for the Drazin inverse and its applications. Linear Algebra Appl, 1997, 258: 179-186

[17] Wei Y, Wu H. The Perturbation of the Drazin inverse and oblique projection. Appl Math Lett, 2000, 13: 77-83

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Higher Education Press and Springer-Verlag Berlin Heidelberg